C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/obcs/orlanski_north.F,v 1.3 2001/09/27 18:13:13 adcroft Exp $ C $Name: $ #include "OBCS_OPTIONS.h" SUBROUTINE ORLANSKI_NORTH( bi, bj, futureTime, I uVel, vVel, wVel, theta, salt, I myThid ) C /==========================================================\ C | SUBROUTINE OBCS_RADIATE | C | o Calculate future boundary data at open boundaries | C | at time = futureTime by applying Orlanski radiation | C | conditions. | C |==========================================================| C | | C \==========================================================/ IMPLICIT NONE C === Global variables === #include "SIZE.h" #include "EEPARAMS.h" #include "PARAMS.h" #include "GRID.h" #include "OBCS.h" #include "ORLANSKI.h" C SPK 6/2/00: Added radiative OBCs for salinity. C SPK 6/6/00: Changed calculation of OB*w. When K=1, the C upstream value is used. For example on the eastern OB: C IF (K.EQ.1) THEN C OBEw(J,K,bi,bj)=wVel(I_obc-1,J,K,bi,bj) C ENDIF C C SPK 7/7/00: 1) Removed OB*w fix (see above). C 2) Added variable CMAX. Maximum diagnosed phase speed is now C clamped to CMAX. For stability of AB-II scheme (CFL) the C (non-dimensional) phase speed must be <0.5 C 3) (Sonya Legg) Changed application of uVel and vVel. C uVel on the western OB is actually applied at I_obc+1 C while vVel on the southern OB is applied at J_obc+1. C 4) (Sonya Legg) Added templates for forced OBs. C C SPK 7/17/00: Non-uniform resolution is now taken into account in diagnosing C phase speeds and time-stepping OB values. CL is still the C non-dimensional phase speed; CVEL is the dimensional phase C speed: CVEL = CL*(dx or dy)/dt, where dx and dy is the C appropriate grid spacings. Note that CMAX (with which CL C is compared) remains non-dimensional. C C SPK 7/18/00: Added code to allow filtering of phase speed following C Blumberg and Kantha. There is now a separate array C CVEL_**, where **=Variable(U,V,T,S,W)Boundary(E,W,N,S) for C the dimensional phase speed. These arrays are initialized to C zero in ini_obcs.F. CVEL_** is filtered according to C CVEL_** = fracCVEL*CVEL(new) + (1-fracCVEL)*CVEL_**(old). C fracCVEL=1.0 turns off filtering. C C SPK 7/26/00: Changed code to average phase speed. A new variable C 'cvelTimeScale' was created. This variable must now be C specified. Then, fracCVEL=deltaT/cvelTimeScale. C Since the goal is to smooth out the 'singularities' in the C diagnosed phase speed, cvelTimeScale could be picked as the C duration of the singular period in the unfiltered case. Thus, C for a plane wave cvelTimeScale might be the time take for the C wave to travel a distance DX, where DX is the width of the region C near which d(phi)/dx is small. C == Routine arguments == INTEGER bi, bj _RL futureTime _RL uVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) _RL vVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) _RL wVel (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) _RL theta(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) _RL salt (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) INTEGER myThid #ifdef ALLOW_ORLANSKI C == Local variables == INTEGER I, K, J_obc _RL CL, ab1, ab2, fracCVEL, f1, f2 ab1 = 1.5 _d 0 + abEps /* Adams-Bashforth coefficients */ ab2 = -0.5 _d 0 - abEps /* CMAX is maximum allowable phase speed-CFL for AB-II */ /* cvelTimeScale is averaging period for phase speed in sec. */ fracCVEL = deltaT/cvelTimeScale /* fraction of new phase speed used*/ f1 = fracCVEL /* dont change this. Set cvelTimeScale */ f2 = 1.0-fracCVEL /* dont change this. set cvelTimeScale */ C Northern OB (Orlanski Radiation Condition) DO K=1,Nr DO I=1-Olx,sNx+Olx J_obc=OB_Jn(I,bi,bj) IF (J_obc.ne.0) THEN C uVel IF ((UN_STORE_2(I,K,bi,bj).eq.0.).and. & (UN_STORE_3(I,K,bi,bj).eq.0.)) THEN CL=0. ELSE CL=-(uVel(I,J_obc-1,K,bi,bj)-UN_STORE_1(I,K,bi,bj))/ & (ab1*UN_STORE_2(I,K,bi,bj) + ab2*UN_STORE_3(I,K,bi,bj)) ENDIF IF (CL.lt.0.) THEN CL=0. ELSEIF (CL.gt.CMAX) THEN CL=CMAX ENDIF CVEL_UN(I,K,bi,bj) = f1*(CL*dyU(I,J_obc-1,bi,bj)/deltaT)+ & f2*CVEL_UN(I,K,bi,bj) C update OBC to next timestep OBNu(I,K,bi,bj)=uVel(I,J_obc,K,bi,bj)- & CVEL_UN(I,K,bi,bj)*(deltaT/dyU(I,J_obc,bi,bj))* & (ab1*(uVel(I,J_obc,K,bi,bj)-uVel(I,J_obc-1,K,bi,bj)) + & ab2*(UN_STORE_4(I,K,bi,bj)-UN_STORE_1(I,K,bi,bj))) C vVel IF ((VN_STORE_2(I,K,bi,bj).eq.0.).and. & (VN_STORE_3(I,K,bi,bj).eq.0.)) THEN CL=0. ELSE CL=-(vVel(I,J_obc-1,K,bi,bj)-VN_STORE_1(I,K,bi,bj))/ & (ab1*VN_STORE_2(I,K,bi,bj) + ab2*VN_STORE_3(I,K,bi,bj)) ENDIF IF (CL.lt.0.) THEN CL=0. ELSEIF (CL.gt.CMAX) THEN CL=CMAX ENDIF CVEL_VN(I,K,bi,bj) = f1*(CL*dyF(I,J_obc-2,bi,bj)/deltaT)+ & f2*CVEL_VN(I,K,bi,bj) C update OBC to next timestep OBNv(I,K,bi,bj)=vVel(I,J_obc,K,bi,bj)- & CVEL_VN(I,K,bi,bj)*(deltaT/dyF(I,J_obc-1,bi,bj))* & (ab1*(vVel(I,J_obc,K,bi,bj)-vVel(I,J_obc-1,K,bi,bj)) + & ab2*(VN_STORE_4(I,K,bi,bj)-VN_STORE_1(I,K,bi,bj))) C Temperature IF ((TN_STORE_2(I,K,bi,bj).eq.0.).and. & (TN_STORE_3(I,K,bi,bj).eq.0.)) THEN CL=0. ELSE CL=-(theta(I,J_obc-1,K,bi,bj)-TN_STORE_1(I,K,bi,bj))/ & (ab1*TN_STORE_2(I,K,bi,bj) + ab2*TN_STORE_3(I,K,bi,bj)) ENDIF IF (CL.lt.0.) THEN CL=0. ELSEIF (CL.gt.CMAX) THEN CL=CMAX ENDIF CVEL_TN(I,K,bi,bj) = f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT)+ & f2*CVEL_TN(I,K,bi,bj) C update OBC to next timestep OBNt(I,K,bi,bj)=theta(I,J_obc,K,bi,bj)- & CVEL_TN(I,K,bi,bj)*(deltaT/dyC(I,J_obc,bi,bj))* & (ab1*(theta(I,J_obc,K,bi,bj)-theta(I,J_obc-1,K,bi,bj))+ & ab2*(TN_STORE_4(I,K,bi,bj)-TN_STORE_1(I,K,bi,bj))) C Salinity IF ((SN_STORE_2(I,K,bi,bj).eq.0.).and. & (SN_STORE_3(I,K,bi,bj).eq.0.)) THEN CL=0. ELSE CL=-(salt(I,J_obc-1,K,bi,bj)-SN_STORE_1(I,K,bi,bj))/ & (ab1*SN_STORE_2(I,K,bi,bj) + ab2*SN_STORE_3(I,K,bi,bj)) ENDIF IF (CL.lt.0.) THEN CL=0. ELSEIF (CL.gt.CMAX) THEN CL=CMAX ENDIF CVEL_SN(I,K,bi,bj) = f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT)+ & f2*CVEL_SN(I,K,bi,bj) C update OBC to next timestep OBNs(I,K,bi,bj)=salt(I,J_obc,K,bi,bj)- & CVEL_SN(I,K,bi,bj)*(deltaT/dyC(I,J_obc,bi,bj))* & (ab1*(salt(I,J_obc,K,bi,bj)-salt(I,J_obc-1,K,bi,bj)) + & ab2*(SN_STORE_4(I,K,bi,bj)-SN_STORE_1(I,K,bi,bj))) C wVel #ifdef ALLOW_NONHYDROSTATIC IF ((WN_STORE_2(I,K,bi,bj).eq.0.).and. & (WN_STORE_3(I,K,bi,bj).eq.0.)) THEN CL=0. ELSE CL=-(wVel(I,J_obc-1,K,bi,bj)-WN_STORE_1(I,K,bi,bj))/ & (ab1*WN_STORE_2(I,K,bi,bj)+ab2*WN_STORE_3(I,K,bi,bj)) ENDIF IF (CL.lt.0.) THEN CL=0. ELSEIF (CL.gt.CMAX) THEN CL=CMAX ENDIF CVEL_WN(I,K,bi,bj)=f1*(CL*dyC(I,J_obc-1,bi,bj)/deltaT) & + f2*CVEL_WN(I,K,bi,bj) C update OBC to next timestep OBNw(I,K,bi,bj)=wVel(I,J_obc,K,bi,bj)- & CVEL_WN(I,K,bi,bj)*(deltaT/dyC(I,J_obc,bi,bj))* & (ab1*(wVel(I,J_obc,K,bi,bj)-wVel(I,J_obc-1,K,bi,bj))+ & ab2*(WN_STORE_4(I,K,bi,bj)-WN_STORE_1(I,K,bi,bj))) #endif C update/save storage arrays C uVel C copy t-1 to t-2 array UN_STORE_3(I,K,bi,bj)=UN_STORE_2(I,K,bi,bj) C copy (current time) t to t-1 arrays UN_STORE_2(I,K,bi,bj)=uVel(I,J_obc-1,K,bi,bj) - & uVel(I,J_obc-2,K,bi,bj) UN_STORE_1(I,K,bi,bj)=uVel(I,J_obc-1,K,bi,bj) UN_STORE_4(I,K,bi,bj)=uVel(I,J_obc,K,bi,bj) C vVel C copy t-1 to t-2 array VN_STORE_3(I,K,bi,bj)=VN_STORE_2(I,K,bi,bj) C copy (current time) t to t-1 arrays VN_STORE_2(I,K,bi,bj)=vVel(I,J_obc-1,K,bi,bj) - & vVel(I,J_obc-2,K,bi,bj) VN_STORE_1(I,K,bi,bj)=vVel(I,J_obc-1,K,bi,bj) VN_STORE_4(I,K,bi,bj)=vVel(I,J_obc,K,bi,bj) C Temperature C copy t-1 to t-2 array TN_STORE_3(I,K,bi,bj)=TN_STORE_2(I,K,bi,bj) C copy (current time) t to t-1 arrays TN_STORE_2(I,K,bi,bj)=theta(I,J_obc-1,K,bi,bj) - & theta(I,J_obc-2,K,bi,bj) TN_STORE_1(I,K,bi,bj)=theta(I,J_obc-1,K,bi,bj) TN_STORE_4(I,K,bi,bj)=theta(I,J_obc,K,bi,bj) C Salinity C copy t-1 to t-2 array SN_STORE_3(I,K,bi,bj)=SN_STORE_2(I,K,bi,bj) C copy (current time) t to t-1 arrays SN_STORE_2(I,K,bi,bj)=salt(I,J_obc-1,K,bi,bj) - & salt(I,J_obc-2,K,bi,bj) SN_STORE_1(I,K,bi,bj)=salt(I,J_obc-1,K,bi,bj) SN_STORE_4(I,K,bi,bj)=salt(I,J_obc,K,bi,bj) C wVel #ifdef ALLOW_NONHYDROSTATIC C copy t-1 to t-2 array WN_STORE_3(I,K,bi,bj)=WN_STORE_2(I,K,bi,bj) C copy (current time) t to t-1 arrays WN_STORE_2(I,K,bi,bj)=wVel(I,J_obc-1,K,bi,bj) - & wVel(I,J_obc-2,K,bi,bj) WN_STORE_1(I,K,bi,bj)=wVel(I,J_obc-1,K,bi,bj) WN_STORE_4(I,K,bi,bj)=wVel(I,J_obc,K,bi,bj) #endif ENDIF ENDDO ENDDO #endif /* ALLOW_ORLANSKI */ RETURN END